# Homework Help: Alternating series test

1. Nov 29, 2008

### kidsmoker

1. The problem statement, all variables and given/known data

Find a sequence $$a_{n}$$ which is non-negative and null but where $$\sum (-1)^{n+1} a_{n}$$ is divergent.

2. Relevant equations

Alternating series test:

Let $$a_{n}$$ be a decreasing sequence of positive real numbers such that $$a_{n}\rightarrowa$$ as $$n\rightarrow\infty$$. Then the series $$\sum (-1)^{n+1} a_{n}$$ converges.

3. The attempt at a solution

I'm a bit confused by this one. If $$a_{n}$$ is non-negative and null then it seems like it's decreasing to zero, in which case it satisfies the alternating series test. So how can the sum diverge?!

Last edited: Nov 29, 2008
2. Nov 29, 2008

### Dick

How about (1,0,1/2,0,1/3,0,1/4,0...)? It's null but nondecreasing. The (-1)^(n+1) doesn't help much does it?

3. Dec 1, 2008

### kidsmoker

Ah yeah i see. So you sort of pad it out with zeros to remove the minus terms. Thanks!